Structure and Performance Analysis of the 7! Robots Generated from an Optimally Fault Tolerant Jacobian

Biyun Xie, Anthony A. Maciejewski

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A measure of local fault tolerance for kinematically redundant robots has previously been defined based on the properties of the singular values of the Jacobian matrix. Based on these measures, one can determine a Jacobian that is optimal. Because these measures are solely based on the singular values of the Jacobian, permutation of the columns does not affect the optimality. Therefore, when one generates a kinematic robot design from this optimal Jacobian, there will be 7! robot designs with the same locally optimal fault tolerant property. The work described here shows how to analyze and organize the kinematic structure of these 7! designs in terms of their Denavit and Hartenberg (DH) parameters. Furthermore, global fault tolerant measures are defined in order to evaluate the different designs. It is shown that robot designs that are very similar in terms of DH parameters, e.g., robots generated from Jacobians where the columns are in reverse order, can have very different global properties. Finally, a computationally efficient approach to calculate the global pre- and post-failure dexterity measures is presented and used to identify two Pareto optimal robot designs. The workspaces for these optimal designs are also shown.

Original languageEnglish
Article number7083369
Pages (from-to)1956-1963
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number4
StatePublished - Oct 2017

Bibliographical note

Publisher Copyright:
© 2016 IEEE.


  • Failure detection and recovery
  • kinematics
  • redundant robots

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Biomedical Engineering
  • Human-Computer Interaction
  • Mechanical Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Control and Optimization
  • Artificial Intelligence


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